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"But my question is, the excessive contribution was from 2023, not 2024 - would it be any problem to carry that in to 2025? "

This would be fine; in fact, it's supposed to work that way - if you can't take as a contribution one year, you can take it in the next.

"if I do return the “mistaken distribution” and remove it as “excessive contribution” now, do I have to pay income tax on the excessive contribution again?"

Yes. The 2023 excess contribution was supposed to have been removed by April 15, 2024. If you remove it at any time after that point, then it will be reported as income with a 20% penalty.

Your choice of #3 does have the following implications:

1. Your 2023 return should have showed excess contributions being carried over to 2024 (which you are going to carry over to 2025). I assume that your 2023 return did not because you said you were going to withdraw it. This means that you will need to amend your 2023 return to generate that carryover (by telling TurboTax that you will not withdraw the excess by April 15 2024).

2. This would generate an entry in the Carryover Worksheet (yes, that's how we communicate things from one year to the next). 

3. But you want to file your 2024 return now. That's OK, because TurboTax asks you in the 2024 HSA interview, "Did you overfund your HSA in 2023?" Answer yes, and then enter the amount of the excess that you know that 2023 is going to show. This will apply the carryover from 2023 to 2024 (I don't know what contributions you already made in 2024 - maybe part of the 2023 carryover can be used in 2024?). 

4. Then when the 2024 TurboTax tells you that you have an excess, TurboTax will limit how much you can withdraw to only excess derived from 2024, not from 2023. Withdraw whatever you can, otherwise let the rest carry over to 2025, where you will finish it off.

5. Fortunately, the filing of 2024 does not depend on amending 2023 first, so file 2024 now, and amend 2023 when you get around to it later this year.